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CSE452 Computer Graphics

CSE452 Computer Graphics. Lecture 6: Projection. Model. Lect 2-3: Images. Lect 17-21: Curves, surfaces, fractals, and dynamic objects. Lect 4-5: Basic shapes. Skeleton of CSE452. Render. Lect 6-9: Camera projection. Lect 10-15: Illumination. Interact. Lect 16:

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CSE452 Computer Graphics

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  1. CSE452 Computer Graphics Lecture 6: Projection

  2. Model Lect 2-3: Images Lect 17-21: Curves, surfaces, fractals, and dynamic objects Lect 4-5: Basic shapes Skeleton of CSE452 Render Lect 6-9: Camera projection Lect 10-15: Illumination Interact Lect 16: User interfaces

  3. A painting based on a mythical tale as told by Pliny the Elder

  4. Planar Geometric Projection A’ A

  5. Classification of Projections Perspective Projection Parallel Projection

  6. Parallel Projections • Preserves object size • Edges parallel to projection plane maintain their lengths after projection • Preserves parallelism • Lines that are parallel stay parallel after projection

  7. Types of Parallel Projection • Orthographic projection • Projectors orthogonal to the view plane • Oblique projection • Projectors not orthogonal to the view plane

  8. Types of Parallel Projection Orthographic Oblique

  9. Multi-view Orthographic Projection • Projection plane is one of coordinate planes “3D Max” software interface

  10. Axonometric Orthographic Projections • Projection plane is not one of coordinate planes Dimetric Isometric

  11. Oblique Projections • Projectors not orthogonal to projection plane • The projection plane is typically parallel to a face of the object • Classified by the angle between projector and plane • Pi/4: Cavalier type • Preserves the lengths of edges orthogonal to projection plane • ArcTan(2): Cabinet type • Halves the lengths of edges orthogonal to projection plane Cavalier: 45 degree Cabinet: arctan(2) =63.4 degree

  12. Examples of Parallel Projections

  13. Parallel Projection in Drawing Earliest known technical drawing: Plan view (orthographic projection) from Mesopotamia, 2150 BC

  14. Perspective Projections • How our eyes see the world • Objects further away look smaller (foreshortening) • Parallel lines may not remain parallel

  15. Vanishing Points • Perspective projection of a group of parallel lines intersects at a single vanishing point • Unless the group is parallel to the projection plane • Why?

  16. 3D line Viewpoint

  17. 3D line • Find P on the viewing plane so that PE is parallel to AB • P,A’,B’ lie on the same line, because of these facts: • A,B,P,E defines a plane. • P,A’,B’ all lie on the plane of ABPE • P,A’,B’ also lie on the viewing plane. • P,A’,B’ all lie on the intersecting line between viewing plane and the plane of ABPE. Viewpoint

  18. Similarly, P,C’,D’ are co-linear for any CD parallel to PE. Conclusion: P is the vanishing point (unless AB is parallel to the viewing plane, in which case P does not exist) Viewpoint

  19. Types of Perspective Projections • Based on number of vanishing points for lines parallel to the three coordinate axes • Determined by # of axes parallel to the viewing plane A unit cube: One-point Perspective (view plane parallel to 2 axes) Two-point Perspective (view plane parallel to 1 axis) Three-point Perspective (view plane not parallel to any axis)

  20. Giotto, Franciscan Rule Approved, 1295-1300

  21. Leonardo da Vinci, The Last Supper, 1495–1498

  22. Jan Vermeer, The Music Lesson, 1662

  23. 3D Reconstruction of The Music Lesson

  24. Classification of Projections

  25. Classification of Projections

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